Discussion:

The market value of a Buydown is the present value of the difference between the amount of the two monthly (or annual) payments. The monthly payment is an annuity so columns 5 and 6 of the compound interest tables are used in this problem.

Present value of a buydown = PV of [Payment #1 minus Payment #2]

Mortgage Problem #3:

Jane is offered a 20 year loan at a 10% rate. The mortgage company will allow an 8% rate for the first 4 years if she pays 50% of the market value of the buydown in advance. If Jane borrows $100,000 and accepts the buydown offer, how much will she have to pay for the buydown.

Solution:

1. | Payment = Mortgage Constant (column 6) x Original Loan Amount (See Problem #1) |

2. | Payment @10% = 0.00965022 x $100,000 = $965.02 |

3. | Payment @8% = 0.00836440 x $100,000 = $836.44 |

4. | Difference in payments = $965.02 - $836.44 = $128.58 |

5. | Present Value of a $128.58 annuity @10 for 4 years = 0.31547080 x $128.58 = $5,070 |

6. | $5,070 x 50% = $2,435 is Jane's cost of the buydown |

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